Initial boundary value problem for fractional p-Laplacian Kirchhoff type equations with logarithmic nonlinearity.
Peng Shi1, Min Jiang1, Fugeng Zeng1
1School of Date Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China.
Mathematical Biosciences and Engineering : MBE
|April 24, 2021
Summary
This study investigates fractional p-Laplacian Kirchhoff equations, revealing solutions exhibit extinction properties and decay rates using logarithmic Sobolev inequality. We also analyzed blow-up and boundedness behaviors.
Area of Science:
- Partial Differential Equations
- Nonlinear Analysis
- Mathematical Physics
Background:
- Fractional calculus extends classical calculus to non-integer orders.
- Kirchhoff-type equations model phenomena in elasticity and fluid dynamics.
- Logarithmic nonlinearities introduce unique challenges in analyzing diffusion processes.
Purpose of the Study:
- Analyze the initial boundary value problem for fractional p-Laplacian Kirchhoff diffusion equations.
- Investigate the extinction property and asymptotic behavior of solutions.
- Examine the blow-up and global boundedness of solutions under specific conditions.
Main Methods:
- Application of the logarithmic Sobolev inequality.
- Techniques for analyzing fractional differential equations.
- Energy methods and a priori estimates.
Main Results:
- Established the extinction property for solutions.
- Derived accurate decay estimates for solutions.
- Characterized the blow-up and global boundedness of solutions.
Conclusions:
- The logarithmic Sobolev inequality is crucial for understanding solution behavior.
- Solutions exhibit predictable extinction and decay patterns.
- The study provides a comprehensive analysis of the qualitative properties of these complex diffusion equations.
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